This one is hard to say, both cards use the 680 PCB, the EVGA exhausts the heat out of the case, the Gigabyte exhausts heat inside the case. Personally I would go EVGA if you plan on doubling up, because the top card will just heat up the bottom card with the Gigabyte variant. As others here already mentioned.
I can't speak for the Gigabyte, but I just got an EVGA FTW and I am very happy with it, I can barely hear the fan at full load (Inside of Storm Trooper case).
I replaced my blown Sapphire 7950 OC with it and the EVGA is definitely the faster card, the AMD had high peak speeds, but they were very unstable, whereas the nVidia constantly had high FPS without the drops in between.
The only reason I swapped cards and dropped another $400+ into a GPU was because Sapphire has the WORST customer service policies on the planet. My card fried (no OCing) after 33 days of purchase and they told me the RMA (which should have been a DOA in the first place) will take 2 months and I will be receiving a refurb instead of a new one, on top of it I had to pay $45 for shipping it to Hong Kong (which I avoided by getting my retailer to ship it out in the end). So that was my rant.
Overall I am VERY happy with the EVGA, I noticed that some people say it's loud because it uses an OEM cooler, my guess is that most people making these claims are either overly sensitive, or do not have personal hands on experience with the FTW. I can't tell you which card is quieter the Gigabyte or the EVGA because I only ever have had hands on experience with the EVGA. Your best bet will be to read the reviews and hopefully someone mentions the in case temps with 2 FTW and 2 Gigabytes inside a HAF X case.